Montaseri, Ghazal; Adhami-Mirhosseini, Aras; Yazdanpanah, Mohammad Javad A mathematical approach to desynchronization of coupled oscillators: application to a neuronal ensemble. (English) Zbl 1280.93040 Int. J. Biomath. 6, No. 2, Article ID 1350009, 17 p. (2013). Summary: Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essential tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchronization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators’ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique. Cited in 2 Documents MSC: 93C10 Nonlinear systems in control theory 92C20 Neural biology 93C95 Application models in control theory Keywords:limit-cycle oscillators; nonlinear output regulation; synchrony suppression; robust stimulation PDFBibTeX XMLCite \textit{G. Montaseri} et al., Int. J. Biomath. 6, No. 2, Article ID 1350009, 17 p. (2013; Zbl 1280.93040) Full Text: DOI References: [1] DOI: 10.1016/j.neunet.2009.08.005 · doi:10.1016/j.neunet.2009.08.005 [2] DOI: 10.1126/science.1223154 · doi:10.1126/science.1223154 [3] DOI: 10.1007/978-1-4612-2020-6 · doi:10.1007/978-1-4612-2020-6 [4] DOI: 10.1016/j.physd.2006.12.004 · Zbl 1120.34024 · doi:10.1016/j.physd.2006.12.004 [5] DOI: 10.1007/s00498-011-0072-9 · Zbl 1238.93035 · doi:10.1007/s00498-011-0072-9 [6] DOI: 10.1142/S0219493705001420 · Zbl 1070.92007 · doi:10.1142/S0219493705001420 [7] DOI: 10.1007/s00791-006-0034-9 · Zbl 05193030 · doi:10.1007/s00791-006-0034-9 [8] DOI: 10.1137/1.9780898718683 · Zbl 1087.93003 · doi:10.1137/1.9780898718683 [9] DOI: 10.1109/9.148359 · Zbl 0767.93042 · doi:10.1109/9.148359 [10] DOI: 10.1007/978-1-84628-615-5 · doi:10.1007/978-1-84628-615-5 [11] DOI: 10.1109/9.45168 · Zbl 0704.93034 · doi:10.1109/9.45168 [12] Khalil H. K., Nonlinear Control Systems (2002) [13] DOI: 10.1007/978-3-642-69689-3 · doi:10.1007/978-3-642-69689-3 [14] DOI: 10.1007/s00422-009-0334-5 · Zbl 1266.92031 · doi:10.1007/s00422-009-0334-5 [15] DOI: 10.1016/j.physd.2007.09.019 · Zbl 1154.34018 · doi:10.1016/j.physd.2007.09.019 [16] DOI: 10.1007/0-8176-4465-2 · doi:10.1007/0-8176-4465-2 [17] DOI: 10.1017/CBO9780511755743 · doi:10.1017/CBO9780511755743 [18] DOI: 10.1007/s00422-006-0066-8 · Zbl 1169.93338 · doi:10.1007/s00422-006-0066-8 [19] DOI: 10.1007/s10867-008-9068-1 · doi:10.1007/s10867-008-9068-1 [20] Popovych O. V., Phys. Rev. E 82 pp 1– (2010) [21] DOI: 10.1103/PhysRevLett.92.114102 · doi:10.1103/PhysRevLett.92.114102 [22] DOI: 10.1103/PhysRevE.70.041904 · doi:10.1103/PhysRevE.70.041904 [23] DOI: 10.1142/S0218127406015842 · Zbl 1154.92307 · doi:10.1142/S0218127406015842 [24] DOI: 10.1016/j.neuron.2011.08.023 · doi:10.1016/j.neuron.2011.08.023 [25] DOI: 10.1142/7139 · doi:10.1142/7139 [26] DOI: 10.1007/s00422-003-0425-7 · Zbl 1084.92009 · doi:10.1007/s00422-003-0425-7 [27] DOI: 10.1007/s10867-008-9081-4 · doi:10.1007/s10867-008-9081-4 [28] DOI: 10.1103/PhysRevE.75.011918 · doi:10.1103/PhysRevE.75.011918 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.